How to join two faces with bevel?
You need to bevel Edges, not faces.

How to:
1) Remove unnecessary geometry (to prevent ugly topology later)
2) Bevel the edges
3) Finish your geometry
4) You're done.  

1) Delete faces
Remove unnecessary faces with Delete > Faces, to prevent n-gons.



2) Bevel edges
Select your edges and bevel them.
Adjust width and number of segments as you need.  




3) Finish your mesh.
To create a new face Press F or go to Vertex > New face from vertices
Keep quads where you can.
Add some new edges like I did :).  



4) You're done.
Result with a Bevel modifier and a Subdivision modifier on top.